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In the upcoming LHC Run 3, starting in 2021, the upgraded Time Projection Chamber (TPC) of the ALICE experiment will record minimum bias Pb-Pb collisions in a continuous readout mode at an interaction rate up to 50 kHz. This corresponds to typically 4-5 overlapping collisions during the electron drift time in the detector. Despite careful tuning of the new quadruple GEM-based readout chambers, which fulfill the design requirement of an ion backflow below 1%, these conditions will lead to space-charge distortions of several centimeters that fluctuate in time. They will be corrected via a calibration procedure that uses the information of the Inner Tracking System (ITS), which is located inside, and the Transition Radiation Detector (TRD) and Time-Of-Flight system (TOF), located around the TPC, respectively. By using such a procedure the intrinsic track resolution of the TPC of a few hundred micrometers can be restored. The required online tracking algorithm for the TRD, which is based on a Kalman filter, is presented. The procedure matches extrapolated ITS-TPC tracks to TRD space-points utilizing GPUs. Subsequently these global tracks are refitted neglecting the TPC information. The residuals of the TPC clusters to the interpolation of the refitted tracks are used to create a map of space-charge distortions. Regular updates of the map compensate for changes in the TPC conditions. The map is applied in the final reconstruction of the data. First performance results of the tracking algorithm will be shown.